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Theorem relprcnfsupp 8222
Description: A proper class is never finitely supported. (Contributed by AV, 7-Jun-2019.)
Assertion
Ref Expression
relprcnfsupp 𝐴 ∈ V → ¬ 𝐴 finSupp 𝑍)

Proof of Theorem relprcnfsupp
StepHypRef Expression
1 relfsupp 8221 . . 3 Rel finSupp
21brrelexi 5118 . 2 (𝐴 finSupp 𝑍𝐴 ∈ V)
32con3i 150 1 𝐴 ∈ V → ¬ 𝐴 finSupp 𝑍)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 1987  Vcvv 3186   class class class wbr 4613   finSupp cfsupp 8219
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4741  ax-nul 4749  ax-pr 4867
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2912  df-rex 2913  df-rab 2916  df-v 3188  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-nul 3892  df-if 4059  df-sn 4149  df-pr 4151  df-op 4155  df-br 4614  df-opab 4674  df-xp 5080  df-rel 5081  df-fsupp 8220
This theorem is referenced by:  fsuppres  8244
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